Height measurement by correlating intensity with position of scanning object along optical axis of a structured illumination microscope

ABSTRACT

A method for imaging an object using a microscope includes obtaining axial response data, the axial response data representative of a relationship between a separation between a top surface of the object and an objective lens of the microscope and an intensity of light reflected by the top surface of the object; positioning the object at a distance from the objective lens that is within a linear region of the axial response data; sequentially illuminating the object with a plurality of periodic patterns; obtaining a plurality of images of the object, each image resulting from the illumination of the object with a corresponding one of the plurality of periodic patterns; determining a reconstructed image of the object based on the plurality of images of the object; and, based on variations in the intensity of the reconstructed image, determining a topographic profile of the top surface of the object.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a divisional of commonly assigned copendingU.S. patent application Ser. No. 12/966,207, which was filed on Dec. 13,2010, by Chau-Hwang Lee for a HEIGHT MEASUREMENT BY CORRELATINGINTENSITY WITH POSITION OF SCANNING OBJECT ALONG OPTICAL AXIS OF ASTRUCTURED ILLUMINATION MICROSCOPE and is hereby incorporated byreference.

The present application is related to the following commonly assignedU.S. Provisional Patent Application Ser. No. 61/286,098, which was filedon Dec. 14, 2009, by Chau-Hwang Lee for a OPTICAL PROFILOMETRY and ishereby incorporated by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to optical surface profilometry.

2. Background Information

High resolution surface profilometry plays an important role innanoscience and biological research. For instance, atomic forcemicroscopy (AFM) can be used to study biomolecular activities in realtime. Direct optical imaging techniques are also useful in biologicalresearch because of their capabilities in wide-field imaging andnon-contact measurement. However, the lateral resolution of opticalimaging systems is generally limited by diffraction to about 0.5λ, whereλ is the wavelength of the imaging light.

Structured illumination microscopy (SIM) is an optical imaging techniquewith improved lateral resolution. In SIM, a periodic excitation patternis projected onto a sample. Multiple images are taken with themodulating pattern shifted to different positions transversely to theoptical axis. The modulated illumination patterns are eliminated fromthe collected images by the mathematical combination of multiple images,enabling the recovery of high spatial frequency information and theformation of high resolution images. Linear SIM provides a lateralresolution of about 0.25λ for fluorescence microscopy; even higherresolution is achievable with saturated SIM. Fluorescence SIM withaxially sectioning ability also provides a resolution of about 0.25λ forone-dimensional or two-dimensional structured imaging.

Fluorescence SIM using a liquid-crystal spatial light modulator (SLM)simplifies the configuration of the microscopy system and improves thestability and imaging speed of the system. In one SIM algorithm, fiveimages are used, with the modulating mesh pattern at a differentposition in each image, to obtain a fluorescence image with a lateralresolution of 0.3λ and an axial resolution of 0.38λ.

SUMMARY OF THE INVENTION

In a general aspect, a method for imaging an object using a microscopeincludes obtaining axial response data, the axial response datarepresentative of a relationship between a separation between a topsurface of the object and an objective lens of the microscope and anintensity of light reflected by the top surface of the object;positioning the object at a distance from the objective lens that iswithin a linear region of the axial response data; sequentiallyilluminating the object with a plurality of periodic patterns; obtaininga plurality of images of the object, each image resulting from theillumination of the object with a corresponding one of the plurality ofperiodic patterns; determining a reconstructed image of the object basedon the plurality of images of the object; and, based on variations inthe intensity of the reconstructed image, determining a topographicprofile of the top surface of the object.

Embodiments may include one or more of the following. The plurality ofperiodic patterns includes interference patterns generated by aplurality of lasers. Sequentially illuminating the object includesadjusting an optical path length of at least one of the plurality oflasers.

Sequentially illuminating the object with a plurality of periodicpatterns includes illuminating the object through a mesh pattern,changing the position of the mesh pattern, and illuminating the objectthrough the repositioned mesh pattern. Changing the position of the meshpattern includes at least one of translating and rotating the pattern.

Sequentially illuminating the object with a plurality of periodicpatterns includes generating a pattern using an electro-optic spatiallight modulator, such as a liquid-crystal spatial light modulator.

The linear region of the axial response data includes a region of thedata in which the relationship between the separation of the top surfaceof the object and the objective lens and the intensity of the reflectedlight is substantially linear. The plurality of images of the object isobtained without changing the separation between the top surface of theobject and the objective lens of the microscope.

In another general aspect, a method for imaging an object using amicroscope includes obtaining a plurality of images of the object, eachimage corresponding to a different separation between a top surface ofthe object and an objective lens of the microscope; for each of aplurality of lateral positions on the top surface of the object,identifying a separation between the top surface of the object and theobjective lens at which the intensity of the image at that lateralposition is maximum; and, based on the identified separations,determining a topographic profile of the top surface of the object.

Embodiments may include one or more of the following. The separation atwhich the intensity of the image is maximum corresponds to an overlapbetween the top surface of the sample and a focal plane of the objectivelens. The topographic profile is further determined based on axialresponse data representative of a relationship between a separationbetween the top surface of the object and the objective lens of themicroscope and an intensity of light reflected by the top surface of theobject. Obtaining a plurality of images of the object includes obtainingat least ten images of the object.

In another general aspect, height measurement using structuredillumination sectioning microscopy is achieved by searching the axialposition of the maximum intensity (peak) of the axial response curve oneach lateral position. By moving the sample and taking tens of opticallysectioned images along the optical axis (z-axis) for a long distance,then recording the axial positions as each lateral position arriving itsmaximum intensity. The maximum intensity arrived when the sample surfacewas overlapped with the focal plane of the objective on the z-axis.Therefore, one can obtain the relative height of the sample surface onthe x-y plane by using this method.

In a further general aspect, height measurement using structuredillumination sectioning microscopy is achieved with the differentialheight measurement concept. This method is suitable for rapidlymeasuring the sample as the surface height variations are within thewidth of the intensity axial response curve. Moving the sample surfaceinto the linear region of the axial response curve of the sectioningmicroscopy when one wants to measure the sample surface profile. In thislinear region, the image intensity is linearly correlated to the heightvariation of the sample. Therefore, when the linear relation of theaxial response curve is obtained (stored into a computer database), thesample surface profile can be immediately translated from the intensityvariations of the image without doing any z-axis scanning process.

Among other advantages, the microscopy techniques described herein allowoptical imaging and profilometry with a lateral resolution smaller thanthe optical diffraction limit and a depth profiling accuracy of lessthan 10 nm. Such high resolution is useful for a number of applications,including visualization of real-time biological processes and theimaging of complex nanostructures. These techniques can be implementedin a straightforward setup.

Other features and advantages of the invention are apparent from thefollowing description and from the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention description below refers to the accompanying drawings, ofwhich:

FIG. 1 is a schematic diagram of an optical nano-profilometry system;

FIG. 2 is an axial response curve of a structured illuminationmicroscope;

FIG. 3 a is a set of images obtained by illuminating a sample with amesh pattern;

FIG. 3 b is a graph of the linear region of the axial response curve ofthe sample of FIG. 3 a.

FIG. 4 a is a conventional bright-field microscopy image of four 80 nmgold particles on a glass substrate;

FIG. 4 b is an image of the particles in FIG. 4 a obtained by structuredillumination microscopy;

FIG. 4 c is is a graph of line profiles along the dashed white lines inthe images of FIGS. 4 a (gray curve) and 4 b (black curve). The dashedcurve represents the summation of two Airy formulas separated by 190 nm;

FIGS. 5 a-c are an atomic force microscopy topography image, aconventional bright-field microscopy image, and a structuredillumination microscopy image, respectively, of a gold wire on a siliconsubstrate; and

FIG. 5 d is a graph of line profiles along the dashed lines of FIGS. 5 a(dashed curve), 5 b (gray curve), and 5 c (black curve).

DETAILED DESCRIPTION OF AN ILLUSTRATIVE EMBODIMENT

Bright-field optical nano-profilometry with sub-diffraction limitlateral resolution can be achieved using structured illuminationmicroscopy (SIM) with axial sectioning. In SIM, a periodic excitationpattern is projected onto a specimen. High spatial frequency informationabout the specimen can be collected into the optical transfer functionof the imaging system. The combination of multiple images, such as fiveimages, each with the modulating excitation patterned positioned at adifferent position with respect to the optical axis of the imagingsystem, enables a lateral resolution of 0.3λ and an axial resolution ofo.38λ to be achieved. SIM is described in greater detail in “Wide-fieldsuper-resolution optical sectioning microscopy using a single spatiallight modulator,” J. Opt. A: Pure Appl. Opt. 11, 015301 (2009), thecontents of which are incorporated herein by reference. By performingaxial sectioning simultaneously with SIM imaging, both a high resolutionimage and an accurate topographical profile of a specimen can beobtained.

Referring to FIG. 1, a specimen 108 is imaged with a structuredillumination microscopy system 100 that includes a light source 102,such as a power-regulated mercury lamp, a solid-state laser, or a lightemitting diode. An electro-optic spatial light modulator, such as aliquid crystal (LC) spatial light modulator 104, and a polarization beamsplitter 106 generate a two-dimensional excitation pattern. Forinstance, the excitation pattern may be a mesh pattern with a period of1.1 μm⁻¹ when projected onto specimen 108. The patterned illuminationlight enters a microscope 110, which may be a conventional wide-fieldoptical microscope, and is focused onto specimen 108 by a high numericalaperture (NA) objective lens 112. The image reflected from specimen 108is captured by a CCD camera 114 or other image recording device (e.g.,an electron multiplying CCD camera, an intensified CCD camera, or a CMOScamera), and processed by a computer 116.

Specimen 108 is disposed on a stage capable of vertical motion, such asa piezoelectric transducer (PZT) stage 118 controlled by a PZT driver120. In another embodiment, the sample is positioned on a stagecontrolled by a stepping or DC motor configured to change the positionof the sample along the optical axis of microscope 110.

To obtain high lateral resolution, multiple SIM images are collected,each image corresponding to a different position of the excitationpattern relative to the optical axis of microscope 110. For instance,the excitation pattern may be translated or rotated with respect to theoptical axis. The number of SIM images used for the reconstruction of ahigh resolution image of the specimen is determined by a processingalgorithm used by computer 116. In general, any image acquisition andprocessing algorithm that is capable of allowing simultaneousacquisition of a high lateral resolution image and a high accuracytopographic profile of the specimen may be used.

In exemplary structured illumination microscope 100, the illuminationpattern generated by LC spatial light modulator 104 can be shiftedtransversely relatively to the optical axis of microscope 110 in realtime, shortening the image acquisition time. In another embodiment,instead of LC spatial light modulator 104, a two-dimensional meshillumination pattern is generated from an interference pattern betweenbeams from two or more lasers. The illumination pattern is shifted byadjusting the optical path lengths of one or more of the laser beams. Inanother embodiment, a two-dimensional mesh illumination pattern isachieved by installing a fixed mesh pattern into the illumination pathof structured illumination microscope 100 and projecting the patternonto the surface of specimen 108. The spatial position or orientation ofthe pattern can be changed by translating or rotating the installedpattern using a translation or rotation stage.

Referring to FIGS. 1 and 2, in axially sectioning SIM, an axial responsecurve 200 relates the position of specimen 108 along the optical axis ofmicroscope 110 with the intensity of the resulting image. A peak 202 ofaxial response curve 200 corresponds to the position of specimen 108 atwhich the focal plane of objective lens 112 overlaps with the topsurface of specimen 108.

In one embodiment, peak 202 of axial response curve 200 is used tolocalize the height of the top surface of specimen 108. Specimen 108 isscanned along the optical axis of objective lens 112 (defined as thez-axis of the system) for a sufficiently long distance, such as severalmicrons. The axial position (i.e., the height) of the specimen at whicha maximum reflected intensity is obtained is recorded for each lateral(x-y) position of the specimen. The recorded heights represent atopographic profile of the top surface of specimen 108 in the x-y plane.The dynamic range of measurement in this embodiment is limited only bythe axial travelling distance of stage 118, but the method is slowbecause of the large number of images that are collected.

In a second embodiment, a surface profile of specimen 108 is obtainedusing differential height measurement. This embodiment is preferable forthe rapid measurement of specimens with surface height variationssmaller than the width of axial response curve 200. In this embodiment,the top surface of specimen 108 is positioned at a distance fromobjective lens 112 that places the specimen in a linear region 204 ofaxial response curve 200. In linear region 204, the signal intensity isproportional to the height of specimen 108. The linear region of axialresponse curve 200 may, for instance, be stored as a database. Thesurface profile of specimen 108 can be determined referring to theintensity values in the stored axial response curve data withoutperforming any z-axis scanning of the specimen. The intensity of eachpixel of an image of specimen 108 can thus be directly correlated to theheight of the specimen at that location, without performing any z-axisscanning of the specimen.

In this embodiment, if the surface of specimen 108 is of heterogeneousreflectivity, a reference image can be acquired when the sample isplaced on the focal plane. This reference image carries only the signalvariation from the heterogeneous reflectivity. The actual heightvariations can thus be obtained by dividing the image intensity capturedin the linear region by the image intensity in the reference image.

The above two methods can both be used in the axially sectioning SIM toachieve sub-diffraction-limit surface profilometry with depth profilingaccuracy better than 10 nm.

Example 1

Referring to FIG. 3 a, a SIM system was used to reconstruct an axiallysectioned super-resolution image of a mesh pattern. A 100×, 1.1 NAwater-immersion objective with a lateral resolution of 260 nm at anillumination wavelength of 475 nm was used. An electron-multiplying CCDcamera captured the resulting images. A mesh pattern was projected ontoa reflective mirror, generating a pattern with a period of 0.5 μm on themirror surface. The mesh pattern was placed at five different positions,each position having a different modulated intensity I and phase Φ_(x),Φ_(y), generating five images I₀-I₄. A super-resolution image wasreconstructed from the five images using an image processing algorithm.The mirror was then scanned along the z-axis of the SIM system (i.e.,along the axis of the illumination light).

Super-resolution images were reconstructed as described above for sevenheight positions of the mirror. Referring to FIG. 3 b, a linearrelationship is seen between the height of the mirror and the intensityof the corresponding super-resolution image. The deviation between themeasured intensity (black squares) and the linear fit to the data (blackline) corresponds to a depth accuracy of 6 nm.

Example 2

Referring to FIGS. 4 a and 4 b, a conventional bright-field microscopyimage of four 80 nm gold particles on a glass substrate and acorresponding super-resolution image obtained by SIM are shown. Thesurface of the glass substrate was placed at the focal plane of the SIMto demonstrate the bright-field super-resolution capability.

Referring to FIG. 4 c, line profiles corresponding to the dashed whitelines in FIGS. 4 a (gray curve) and 4 b (black curve) are shown. Anintensity dip is observed in the profile obtained from the SIM image,indicating that two adjacent 80 nm particles can be resolved using SIM.Conventional bright-field microscopy does not resolve the two adjacentparticles.

The Airy formula, I(r)=[2J₁(r)/r]², where J₁ is the 1^(st) order Besselfunction of the first kind, is used to estimate the distance between thetwo particles. The intensity dip can be fitted by the summation of twoAiry formulas of 175 nm width (FWHM) and separated by 190 nm. Thesummation is shown as the dashed curve in FIG. 4 c. After deconvolvingthe particle diameter (80 nm), a lateral resolution of 155 nm isobtained, which is about 33% of the illumination wavelength.

Example 3

A gold wire is used to demonstrate the depth profiling accuracy of SIM.This wire was fabricated by using electron-beam lithography and alift-off process on a silicon substrate. Referring to the AFM topographyimage in FIG. 5 a, the width and height of the wire are 450 nm and 115nm, respectively. A conventional bright-field image of the wire, shownin FIG. 5 b, gives a width of about 770 nm due to diffraction effects.The edge response from 10% to 90% of the intensity variation on the wireis about 240 nm, close to the optical resolution of the objective (260nm). The scattering from the edges of the wire makes a dark outline inthe bright-field image. The effect of scattering or inhomogeneousreflectivities can be removed by dividing image intensity obtained inthe linear region of the axial response curve with the image intensityobtained on the focal plane.

After the calibration of the signal intensity to the height variations,the super-resolution topography of the gold wire is obtained, as shownin FIG. 5 c. The gray levels represent a range of heights from 0 to 200nm.

FIG. 5 d shows that the edge response of this wire is ˜140 nm,corresponding to about 30% of the illumination wavelength. The heightmeasured by SINAP is ˜120 nm, close to that measured by AFM.

It is to be understood that the foregoing description is intended toillustrate and not to limit the scope of the invention, which is definedby the scope of the appended claims. Other embodiments are within thescope of the following claims.

What is claimed is:
 1. A method for differential height measurement ofan object using structured illumination sectioning microscopy,comprising: moving a surface of the object into a linear region of axialresponse curve of a microscope configured for structured illuminationsectioning microscopy, wherein the intensity of an image is linearlycorrelated to a height variation of the object in the linear region ofthe axial response curve; obtaining an image of the surface of theobject; and determining a profile of the surface of the object based onintensity variations in the obtained image without scanning the objectalong an optical axis of the microscope.
 2. The method of claim 1,wherein the axial response curve is stored in a computer database.